Axiom ax-bdsb 13704

Description: A formula resulting from proper substitution in a bounded formula is bounded. This probably cannot be proved from the other axioms, since neither the definiens in df-sb 1751, nor probably any other equivalent formula, is syntactically bounded. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdsb.1	⊢ BOUNDED 𝜑

Assertion

Ref	Expression
ax-bdsb	⊢ BOUNDED [𝑦 / 𝑥]𝜑

Detailed syntax breakdown of Axiom ax-bdsb

Step	Hyp	Ref	Expression
1		wph	. . 3 wff 𝜑
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4	1, 2, 3	wsb 1750	. 2 wff [𝑦 / 𝑥]𝜑
5	4	wbd 13694	1 wff BOUNDED [𝑦 / 𝑥]𝜑

This axiom is referenced by:  bdab  13720  bdph  13732  bdsbc  13740  bdcriota  13765